To get this achievement you just need to get an overall A rank on the current Dream you are on.
Watch the videos of their respective Dreams and copy and improve on them. If you get a rank that is not an A on a Mare then don't fret, just make sure you have an A or a B before getting to the boss. If you get an A on all Mares then you still aren't safe as you can go down on your overall rank by taking too much time fighting/getting hit by bosses. If you get to the boss with a B do good and you just might come out with an A.
I got my last A rank with Elliot on Twin Seeds so the achievement unlocked after the credits for me.